Field of the Invention
The present invention relates generally to alignment and classification procedures and more specifically to alignment and classification procedures without a dependence on reference elements.
Background Information
The 3D (3 dimensional) structures of macromolecules can be investigated by single particle analysis, a powerful technique of electron microscopy that provides more penetrating structural analyses of macromolecules whose x-ray crystallography is problematical. Resolution and analyses of molecular interactions and conformational changes, using single particle analysis, have been advancing in pace with the image processing methods employed (Ueno and Sato, 2001). Such methods are needed because imaged macromolecules are obscured by noise backgrounds (with SIN ratios [SNR] often below unity). Noise has its origin partly in the low irradiation levels used to minimize specimen damage. To attenuate noise, one must average the 2D images with the same 3D orientations, a process requiring optimal alignments among the gallery of data set images. Signals then reinforce one another, and noise tends to average out.
As with other techniques of 3D reconstruction, 2D image alignment is critical when applying the RCT (random conical tilt) method to fixed particles, imaged either “face up” or “face down” in a membrane bilayer or film. To recover 3D information coherently, one must know the rotational orientation of each data set image in the plane of the bilayer. This is normally accomplished by bringing untilted images (those viewed “head on” at 0°) into a common rotational alignment. Once relative rotational orientations (the amounts of rotation of given images required to bring them into common alignment) are known for untilted images, they also become known for tilted images, because of pairwise imaging. Single particle analysis should, in principle, achieve atomic resolution. In practice, however, various circumstances prevent this.
Normally, one assumes the existence of a prototype reference image, against which the data set images can be aligned. However, this assumption is unjustified for inhomogeneous data sets. Another problem is that alignments are biased by the choice of reference images. One method to reduce this bias is to average the images aligned to a particular reference, to yield a revised reference (Penczek et al., 1992). However, when the images have a poor SNR, or represent different views of the same macromolecule, this procedure yields a final averaged reference that shares features of the original reference. “Iterative reference free alignment,” selects and aligns two images at random. The process is then repeated with a third selected image, etc., until the data set images have been exhausted (Penczek et al., 1992). However, because the order of selection biases results, the process is repeated with random orders of selection, thereby reducing the bias because this method uses a changing global average for reference, it is not strictly reference free (van Heel et al., 2000).
The “state of the art” technique for generating and aligning reference images representing different views of a data set, is designated “Multivariable Statistical Analysis/Multi Reference Alignment” (MSA/MRA; see Zampighi et al., 2004). Some variations between data set images may not reflect structural differences, but merely positional differences (e.g., in plane rotational orientation, in the case of RCT). For that reason, it is undesirable, when classifying data sets, to consider in plane rotational differences to be valid. Consequently, before classification, images must be brought into mutual rotational alignment, thereby eliminating particle orientation as an independent classification variable.
However, alignments using correlation based techniques are only well defined operations when galleries of images are homogeneous. But to produce representative classes, data set images must first be aligned, which requires an initial set of representative classes. To cope with this “circularity,” workers have resorted to iterative cycles of classification and alignment using MSA/MRA, until results stabilize. However, this procedure does not guarantee attainment of the global minimum of the “energy” function. In addition to these shortcomings, MSA/MRA hinges on subjective operator choices of many critical free variables that impact the final result. Consequently, such results typically are operator dependent. Finally, MSA/MRA often consumes months of processing (Bonetta, 2005).